Transient magneto-peristaltic flow of couple stress biofluids: A magneto-hydro-dynamical study on digestive transport phenomena

Magnetic fields are increasingly being utilized in endoscopy and gastric transport control. In this regard, the present study investigates the influence of a transverse magnetic field in the transient peristaltic rheological transport. An electrically-conducting couple stress non-Newtonian model is employed to accurately simulate physiological fluids in peristaltic flow through a sinusoidally contracting channel of finite length. This model is designed for computing the intra-bolus oesophageal and intestinal pressures during the movement of food bolus in the digestive system under magneto-hydro-dynamic effects. Long wavelength and low Reynolds number approximations have been employed to reduce the governing equations from nonlinear to linear form, this being a valid approach for creeping flows which characterizes physiological dynamics. Analytical approximate solutions for axial velocity, transverse velocity, pressure gradient, local wall shear stress and volumetric flow rate are obtained for the non-dimensional conservation equations subject to appropriate boundary conditions. The effects of couple stress parameter and transverse magnetic field on the velocity profile, pressure distribution, local wall shear stress and the averaged flow rate are discussed with the aid of computational results. The comparative study of non-integral and integral number of waves propagating along the finite length channel is also presented. Magnetic field and non-Newtonian properties are found to strongly influence peristaltic transport.     

Numerical simulation of peristaltic flow of a biorheological fluid with shear-dependent viscosity in a curved channel

Peristaltic motion of a non-Newtonian Carreau fluid is analyzed in a curved channel under the long wavelength and low Reynolds number assumptions, as a simulation of digestive transport. The flow regime is shown to be governed by a dimensionless fourth-order, nonlinear, ordinary differential equation subject to no-slip wall boundary conditions. A well-tested finite difference method based on an iterative scheme is employed for the solution of the boundary value problem. The important phenomena of pumping and trapping associated with the peristaltic motion are investigated for various values of rheological parameters of Carreau fluid and curvature of the channel. An increase in Weissenberg number is found to generate a small eddy in the vicinity of the lower wall of the channel, which is enhanced with further increase in Weissenberg number. For shear-thinning bio-fluids (power-law rheological index, n < 1) greater Weissenberg number displaces the maximum velocity toward the upper wall. For shear-thickening bio-fluids, the velocity amplitude is enhanced markedly with increasing Weissenberg number.     

A mathematical simulation of the ureter: effects of the model parameters on ureteral pressure/flow relations

Ureteral peristaltic mechanism facilitates urine transport from the kidney to the bladder. Numerical analysis of the peristaltic flow in the ureter aims to further our understanding of the reflux phenomenon and other ureteral abnormalities. Fluid-structure interaction (FSI) plays an important role in accuracy of this approach and the arbitrary Lagrangian-Eulerian (ALE) formulation is a strong method to analyze the coupled fluid-structure interaction between the compliant wall and the surrounding fluid. This formulation, however, was not used in previous studies of peristalsis in living organisms. In the present investigation, a numerical simulation is introduced and solved through ALE formulation to perform the ureteral flow and stress analysis. The incompressible Navier-Stokes equations are used as the governing equations for the fluid, and a linear elastic model is utilized for the compliant wall. The wall stimulation is modeled by nonlinear contact analysis using a rigid contact surface since an appropriate model for simulation of ureteral peristalsis needs to contain cell-to-cell wall stimulation. In contrast to previous studies, the wall displacements are not predetermined in the presented model of this finite-length compliant tube, neither the peristalsis needs to be periodic. Moreover, the temporal changes of ureteral wall intraluminal shear stress during peristalsis are included in our study. Iterative computing of two-way coupling is used to solve the governing equations. Two phases of nonperistaltic and peristaltic transport of urine in the ureter are discussed. Results are obtained following an analysis of the effects of the ureteral wall compliance, the pressure difference between the ureteral inlet and outlet, the maximum height of the contraction wave, the contraction wave velocity, and the number of contraction waves on the ureteral outlet flow. The results indicate that the proximal part of the ureter is prone to a higher shear stress during peristalsis compared with its middle and distal parts. It is also shown that the peristalsis is more efficient as the maximum height of the contraction wave increases. Finally, it is concluded that improper function of ureteropelvic junction results in the passage of part of urine back flow even in the case of slow start-up of the peristaltic contraction wave.     

A mathematical model for the peristaltic flow of chyme movement in small intestine

A mathematical model based on viscoelastic fluid (fractional Oldroyd-B model) flow is considered for the peristaltic flow of chyme in small intestine, which is assumed to be in the form of an inclined cylindrical tube. The peristaltic flow of chyme is modeled more realistically by assuming that the peristaltic rush wave is a sinusoidal wave, which propagates along the tube. The governing equations are simplified by making the assumptions of long wavelength and low Reynolds number. Analytical approximate solutions of problem are obtained by using homotopy analysis method and convergence of the obtained series solution is properly checked. For the realistic values of the emerging parameters such as fractional parameters, relaxation time, retardation time, Reynolds number, Froude number and inclination of tube, the numerical results for the pressure difference and the frictional force across one wavelength are computed and discussed the roles played by these parameters during the peristaltic flow. On the basis of this study, it is found that the first fractional parameter, relaxation time and Froude number resist the movement of chyme, while, the second fractional parameter, retardation time, Reynolds number and inclination of tube favour the movement of chyme through the small intestine during pumping. It is further revealed that size of trapped bolus reduces with increasing the amplitude ratio whereas it is unaltered with other parameters.     

Peristaltic transport in a channel with a porous peripheral layer: model of a flow in gastrointestinal tract

Peristaltic transport in a two dimensional channel, filled with a porous medium in the peripheral region and a Newtonian fluid in the core region, is studied under the assumptions of long wavelength and low Reynolds number. The fluid flow is investigated in the waveframe of reference moving with the velocity of the peristaltic wave. Brinkman extended Darcy equation is utilized to model the flow in the porous layer. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. A shear-stress jump boundary condition is used at the interface. The physical quantities of importance in peristaltic transport like pumping, trapping, reflux and axial velocity are discussed for various parameters of interest governing the flow like Darcy number, porosity, permeability, effective viscosity etc. It is observed that the peristalsis works as a pump against greater pressure in two-layered model with a porous medium compared with a viscous fluid in the peripheral layer. Increasing Darcy number Da decreases the pumping and increasing shear stress jump constant beta results in increasing the pumping. The limits on the time averaged flux Q for trapping in the core layer are obtained. The discussion on pumping, trapping and reflux may be helpful in understanding some of the fluid dynamic aspects of the transport of chyme in gastrointestinal tract.     

Mixed Convection Peristaltic Flow of Third Order Nanofluid with an Induced Magnetic Field

This research is concerned with the peristaltic flow of third order nanofluid in an asymmetric channel. The governing equations of third order nanofluid are modelled in wave frame of reference. Effect of induced magnetic field is considered. Long wavelength and low Reynolds number situation is tackled. Numerical solutions of the governing problem are computed and analyzed. The effects of Brownian motion and thermophoretic diffusion of nano particles are particularly emphasized. Physical quantities such as velocity, pressure rise, temperature, induced magnetic field and concentration distributions are discussed.     

Influence of Hall Current and Viscous Dissipation on Pressure Driven Flow of Pseudoplastic Fluid with Heat Generation: A Mathematical Study

In this paper, we study the influence of heat sink (or source) on the peristaltic motion of pseudoplastic fluid in the presence of Hall current, where channel walls are non-conducting in nature. Flow analysis has been carried out under the approximations of a low Reynolds number and long wavelength. Coupled equations are solved using shooting method for numerical solution for the axial velocity function, temperature and pressure gradient distributions. We analyze the influence of various interesting parameters on flow quantities. The present study can be considered as a mathematical presentation of the dynamics of physiological organs with stones.     

Grinding Microorganisms with a Peristaltic Pump

The Randolph Co. model 610 peristaltic, ⅛-hp pump was effective for preparative purposes in disrupting baker's yeast and spores of Bacillus globigii when suspended with glass beads. Best results were obtained with use of a slurry just fluid enough to flow through tubing while stirred. Beads of 0.2 and 0.1 mm were used to best advantage for the yeast cells and spores, respectively. Yeast cells were disrupted completely within 15 min, and the spores in 10 to 30 min. Temperature and surface denaturation are readily controlled, and the system is easily modified for use with large quantities of microorganisms.     

Soret and Dufour Effects on MHD Peristaltic Flow of Jeffrey Fluid in a Rotating System with Porous Medium

The objective of present paper is to examine the peristaltic flow of magnetohydrodynamic (MHD) Jeffrey fluid saturating porous space in a channel through rotating frame. Unlike the previous attempts, the flow formulation is based upon modified Darcy''s law porous medium effect in Jeffrey fluid situation. In addition the impacts due to Soret and Dufour effects in the radiative peristaltic flow are accounted. Rosseland’s approximation has been utilized for the thermal radiative heat flux. Lubrication approach is implemented for the simplification. Resulting problems are solved for the stream function, temperature and concentration. Graphical results are prepared and analyzed for different parameters of interest entering into the problems.     

Comparison of detector systems in oxidative stripping potentiometry

For oxidative stripping potentiometry (OSP) measurement, the achievement of reliable results is highly dependent upon the transport of oxidant to the electrode surface and, as a consequence, careful hydrodynamic control is crucial for reproducibility. Two types of detector system, batch and flow, with three different electrode systems, a standard voltammetric magnetic stirrer cell assembly, an voltammetric cell with optically controlled stirrer and a thin layer flow cell with peristaltic pump were compared. In the sensitivity studies, the static stripping procedure enhanced the sensitivity of the measurement compared to forced convection stripping. The use of a flow cell and peristaltic pump provided all the flexibility needed for OSP measurement. The sensitivity can be improved using the combination of fast deposition and slow stripping flow rates. From the viewpoint of reproducibility of the signals, excellent results were obtained for the use of the flow cell with peristaltic pump.     

A sterile, regulated, pulsation-dampened precision dosing system for biomedical technics

For sterile continuous metering of small and very small flow rates delivered by peristaltic pump, a gravimetric control system which permits a high accuracy of mass flow is described. This is achieved by a digital PI controller and a digital filter with which the very accurate signal from a high precision electronic scale is filtered. In addition proposals are made for solving the problem of refilling the reservoir and for compensating the pulsations caused by the peristaltic pump.     

Peristaltic flow of Walter’s B fluid in a uniform inclined tube

In this investigation, peristaltic flow of Walter’s B fluid in a uniform inclined tube is discussed. The formulation of the problem is made in a cylindrical coordinate system. The analytical solutions have been calculated by using a regular perturbation method by taking δ as the perturbation parameter. The expressions for pressure rise and friction forces were calculated using numerical integration. The graphical results are presented to discuss the various physical quantities of the Walter’s B fluid parameter α, amplitude ratio φ, angle of inclination β and wave length δ.     

Asymptotic method for peristaltic transport

The purpose of this paper is to justify an asymptotic method developed for the study of peristaltic transport in a tube of arbitrary cross section. Within the framework of long wave approximation, the three-dimensional nonlinear Navier-Stokes equations are reduced to a sequence of two-dimensional linear boundary value problems of Laplace and biharmonic operators. It is shown that, if a Reynolds number is less than some constant, the solution of the approximate equations is indeed an asymptotic approximation to the exact solution of the problem as the ratio of the maximum radius of the tube to the wave length of the peristaltic motion of the wall tends to zero, and the error estimates are expressed inL ₂ norms. Furthermore, under the same condition the exact solution is shown to be unique and stable under arbitrary perturbation of spatially periodic disturbance. Application of the stability condition to peristaltic transport in a tube of circular cross section is given.     

Flow fields generated by peristaltic reflex in isolated guinea pig ileum: impact of contraction depth and shoulders

The guinea pig ileum responds to distension with characteristic wall movements, luminal pressure gradients, and outflow (the peristaltic reflex). To date, little is known about whether the peristaltic reflex generates flow events other than laminar flow. Here we used a numerical method to solve for the flow generated by moving walls to assess occlusive contractions (case 1), nonocclusive contractions (case 2), and contractions with steep shoulders (case 3) for which visual parameters of wall movements are published. We found that all three contraction cases produced pressure differentials across the coapting segment, downstream and reverse flow, and vortical flow patterns that redistributed particles and mixed liquids. Contractions generated pressures and shear stresses, particularly along the moving section of the wall. The nonocclusive contraction was much less effective than the occlusive contraction with the steep shoulders; the occlusive contraction with flat shoulders had an intermediate effect. Our analysis shows that even peristaltic contractions produce not only laminar flow but also many flow events likely to promote digestion and absorption. The visual patterns of contractions impact the patterns of luminal flow, and precise definition of wall movements is critical to quantify the fluid mechanical consequences of intestinal contractions.     

Mathematica numerical simulation of peristaltic biophysical transport of a fractional viscoelastic fluid through an inclined cylindrical tube

This paper studies the peristaltic transport of a viscoelastic fluid (with the fractional second-grade model) through an inclined cylindrical tube. The wall of the tube is modelled as a sinusoidal wave. The flow analysis is presented under the assumptions of long wave length and low Reynolds number. Caputo's definition of fractional derivative is used to formulate the fractional differentiation. Analytical solutions are developed for the normalized momentum equations. Expressions are also derived for the pressure, frictional force, and the relationship between the flow rate and pressure gradient. Mathematica numerical computations are then performed. The results are plotted and analysed for different values of fractional parameter, material constant, inclination angle, Reynolds number, Froude number and peristaltic wave amplitude. It is found that fractional parameter and Froude number resist the flow pattern while material constant, Reynolds number, inclination of angle and amplitude aid the peristaltic flow. Furthermore, frictional force and pressure demonstrate the opposite behaviour under the influence of the relevant parameters emerging in the equations of motion. The study has applications in uretral biophysics, and also potential use in peristaltic pumping of petroleum viscoelastic bio-surfactants in chemical engineering and astronautical applications involving conveyance of non-Newtonian fluids (e.g. lubricants) against gravity and in conduits with deformable walls.     

Peristaltic flow of a couple stress fluid in an asymmetric channel

This paper presents an analysis of the peristaltic flow of a couple stress fluid in an asymmetric channel. The asymmetric nature of the flow is introduced through the peristaltic waves of different amplitudes and phases on the channel walls. Mathematical modelling corresponding to a two-dimensional flow has been carried out. The flow analysis is presented under long wavelength and low Reynolds number approximations. Closed form solutions for the axial velocity, stream function and the axial pressure gradient are given. Numerical computations have been carried out for the pressure rise per wavelength, friction forces and trapping. It is noted that there is a decrease in the pressure when the couple stress fluid parameter increases. The variation of the couple stress fluid parameter with the size of the trapped bolus is also similar to that of pressure. Furthermore, the friction force on the lower channel wall is greater than that on the upper channel wall.     

Blood flow augmentation by intrinsic venular contraction in vivo

Venomotion, spontaneous cyclic contractions of venules, was first observed in the bat wing 160 years ago. Of all the functional roles proposed since then, propulsion of blood by venomotion remains the most controversial. Common animal models that require anesthesia and surgery have failed to provide evidence for venular pumping of blood. To determine whether venomotion actively pumps blood in a minimally invasive, unanesthetized animal model, we reintroduced the batwing model. We evaluated the temporal and functional relationship between the venous contraction cycle and blood flow and luminal pressure. Furthermore, we determined the effect of inhibiting venomotion on blood flow. We found that the active venous contractions produced an increase in the blood flow and exhibited temporal vessel diameter-blood velocity and pressure relationships characteristic of a peristaltic pump. The presence of valves, a characteristic of reciprocating pumps, enhances the efficiency of the venular peristaltic pump by preventing retrograde flow. Instead of increasing blood flow by decreasing passive resistance, venular dilation with locally applied sodium nitroprusside decreased blood flow. Taken together, these observations provide evidence for active venular pumping of blood. Although strong venomotion may be unique to bats, venomotion has also been inferred from venous pressure oscillations in other animal models. The conventional paradigm of microvascular pressure and flow regulation assumes venules only act as passive resistors, a proposition that must be reevaluated in the presence of significant venomotion.     

Salt-water coupling in leaky epithelia

Summary The theory of quasi-isotonic transport by cellular osmosis (the standing-gradient theory) has been challenged on the grounds that the osmotic permeabilities of the mucosal and interspace membranes are too low; if they were as high as the theory requires then the osmotic permeability of the whole epithelium would be 2–3 orders of magnitude higher than observed. This objection has basically been accepted for it is now claimed that these enormous permeabilities do exist, but are masked by unstirred-layer effects; I show that this is incorrect because unstirredlayer corrections are small and that the situation has not changed since 1975.The view that the route of fluid transport is junctional is replacing the cellular theory, and trans-junctional water flows seem to account for major fractions of the flow in various epithelia. I argue on grounds of general theory that these are unlikely to be osmotic flows because the junctional pores cannot satisfy both the osmotic and diffusive properties required of them, but the basic osmotic theory is also rather vague here.Non-osmotic theories, if junctional flow is accepted, must be either electro-kinetic or peristaltic.     

Peristaltic biofluids flow through vertical porous human vessels using third-grade non-Newtonian fluids model

In this paper, the heat and flow characteristic of third-grade non-Newtonian biofluids flow through a vertical porous human vessel due to peristaltic wall motion are studied. The third-grade model can describe shear thinning (or shear thickening) and normal stress differences, which is acceptable for biofluids modeling. In order to solve the governing equations, the assumption of long-wavelength approximation is utilized. This hypothesis emphasizes that the wavelength of the peristaltic wall motion is large in comparison with the radius of the human vessel, which is widely acceptable in biological investigations. The analytical perturbation method is employed to solve the governing equations. Consequently, analytical expressions for the velocity profile, shear stress, temperature field, and biofluid flow rate are obtained. In addition, the effects of the governing parameters such as the third-grade non-Newtonian parameter, Grashof Number, Eckert number, and porosity, on the results are examined.     

A Quantitative Investigation of a Peristaltic Model for Phloem Translocation

An analysis is made of a peristaltic model of phloem translocationIt is postulated that the periodic action of contractile orbending organelles drive a longitudinal flow of solution withintubules which connect sieve pores in successive sieve plates Plausible values are assumed for the velocity of propagationof the contraction wave, the frequency, the amplitude, and theviscosity of the solution and its concentration. Using relationswhich describe peristaltic flow, predictions are made for thevalues of parameters such as the velocity of solution, the drivingpressure, and rate of energy dissipation. These predicted valuesare seen to be reasonable when compared with the known propertiesof other biological contractile systems. Thus the model is quantitativelyacceptable.